Digit Maps

Michael De Vlieger’s digit maps for bases 2 ≤ r ≤ 60. Number bases r occupy the vertical axis. Each row presents the set of digits n of r, from 0 to ω = (r - 1). Digit-0 represents congruence with r; the case where digit-0 represents actual zero is ignored for the purpose of the digit map. Purple represents the unit digit (digit-1, both a divisor of and coprime to r). Red represents divisors of r. Orange represents semidivisors of r. A semidivisor is a regular digit that does not divide r evenly. Yellow represents semitotatives. The semitotative is a digit neither a divisor nor coprime to r that is composed of at least one prime divisor and at least one prime totative of r. Light blue represents totatives of r related to the omega digit, (r - 1). Light green represents totatives of r related to the alpha number, (r + 1). Light purple represents digit-2 in odd bases, related both to omega and alpha. Gray represents “opaque” totatives, related neither to omega nor alpha.

This page last modified Wednesday 5 October 2011.